Critical Fluctuations In A Dynamically Expanding Heavy-Ion Collision

For the discovery of the QCD critical point it is crucial to develop dynamical models of the fluctuations of the net baryon number that can be embedded in simulations of heavy-ion collisions. In this proceeding, we study the dynamical formation of the critical fluctuations of the net-baryon number near the QCD critical point and their survival in the late stages in an expanding system. The stochastic diffusion equation with a non-linear free energy functional is employed for describing the evolution of conserved-charge fluctuations along trajectories in the crossover and first-order transition regions near the QCD critical point.